From 9cc63f8bcd560c760d0b12e15bba8f81c86237cf Mon Sep 17 00:00:00 2001 From: "Paul E. McKenney" Date: Fri, 14 Aug 2026 15:43:51 -0700 Subject: Merge branches 'expcb.2026.07.24a', 'misc.2026.07.30a', 'rcu-tasks.2026.07.30a', 'srcu.2026.08.11a' and 'torture.2026.08.14a' into HEAD Changes: Make expedited grace periods expedite normal RCU callbacks Miscellaneous fixes: * Improve diagnostic output with character task states. * Mark accesses to inform KCSAN of concurrency design. * Move from kmalloc() to kmalloc_obj(). * Documentation updates. * Improve handling of RCU deferred quiescent states. * Clean up unused function arguments and structure fields. * Reduce show_rcu_gp_kthreads() stack space. Tasks RCU updates: * Clean up after SRCU re-implementation of Tasks Trace RCU. * Mark accesses to inform KCSAN of concurrency design. * Add ->lazy_timer status to diagnostic output. * Remove an unnecessary memory barrier. * Fix a data race, courtesy of KCSAN. * Documentation updates. * Convert cond_resched_tasks_rcu_qs() from macro to static inline function. SRCU updates: * Add Rust helpers for SRCU. * Avoid losing queued work at cleanup_srcu_struct() time. Torture-test updates: * Preparation work for immediate RCU priority deboosting. * Test RCU readers from real interrupt handlers (as opposed to softirq). * Simplify code through use of cpumask_next_wrap(). * Improve diagnostic output with character task states. * Add rcutorture.nwriters parameter to allow lightweight stall testing, and rcutorture.stall_only to make doing so easier. * Test an RCU Tasks Trace grace period implying an RCU grace period. * Make RCU Tasks Trace torturing track reader batches. * Fix a data race, courtesy of KCSAN. * Plug a shuffle_tmp_mask memory leak on kthread spawn failure. --- lib/math/rational.c | 112 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 112 insertions(+) create mode 100644 lib/math/rational.c (limited to 'lib/math/rational.c') diff --git a/lib/math/rational.c b/lib/math/rational.c new file mode 100644 index 000000000..d2c34e629 --- /dev/null +++ b/lib/math/rational.c @@ -0,0 +1,112 @@ +// SPDX-License-Identifier: GPL-2.0 +/* + * rational fractions + * + * Copyright (C) 2009 emlix GmbH, Oskar Schirmer + * Copyright (C) 2019 Trent Piepho + * + * helper functions when coping with rational numbers + */ + +#include +#include +#include +#include +#include +#include + +/* + * calculate best rational approximation for a given fraction + * taking into account restricted register size, e.g. to find + * appropriate values for a pll with 5 bit denominator and + * 8 bit numerator register fields, trying to set up with a + * frequency ratio of 3.1415, one would say: + * + * rational_best_approximation(31415, 10000, + * (1 << 8) - 1, (1 << 5) - 1, &n, &d); + * + * you may look at given_numerator as a fixed point number, + * with the fractional part size described in given_denominator. + * + * for theoretical background, see: + * https://en.wikipedia.org/wiki/Continued_fraction + */ + +void rational_best_approximation( + unsigned long given_numerator, unsigned long given_denominator, + unsigned long max_numerator, unsigned long max_denominator, + unsigned long *best_numerator, unsigned long *best_denominator) +{ + /* n/d is the starting rational, which is continually + * decreased each iteration using the Euclidean algorithm. + * + * dp is the value of d from the prior iteration. + * + * n2/d2, n1/d1, and n0/d0 are our successively more accurate + * approximations of the rational. They are, respectively, + * the current, previous, and two prior iterations of it. + * + * a is current term of the continued fraction. + */ + unsigned long n, d, n0, d0, n1, d1, n2, d2; + n = given_numerator; + d = given_denominator; + n0 = d1 = 0; + n1 = d0 = 1; + + for (;;) { + unsigned long dp, a; + + if (d == 0) + break; + /* Find next term in continued fraction, 'a', via + * Euclidean algorithm. + */ + dp = d; + a = n / d; + d = n % d; + n = dp; + + /* Calculate the current rational approximation (aka + * convergent), n2/d2, using the term just found and + * the two prior approximations. + */ + n2 = n0 + a * n1; + d2 = d0 + a * d1; + + /* If the current convergent exceeds the maxes, then + * return either the previous convergent or the + * largest semi-convergent, the final term of which is + * found below as 't'. + */ + if ((n2 > max_numerator) || (d2 > max_denominator)) { + unsigned long t = ULONG_MAX; + + if (d1) + t = (max_denominator - d0) / d1; + if (n1) + t = min(t, (max_numerator - n0) / n1); + + /* This tests if the semi-convergent is closer than the previous + * convergent. If d1 is zero there is no previous convergent as this + * is the 1st iteration, so always choose the semi-convergent. + */ + if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) { + n1 = n0 + t * n1; + d1 = d0 + t * d1; + } + break; + } + n0 = n1; + n1 = n2; + d0 = d1; + d1 = d2; + } + *best_numerator = n1; + *best_denominator = d1; +} + +EXPORT_SYMBOL(rational_best_approximation); + +MODULE_DESCRIPTION("Rational fraction support library"); +MODULE_LICENSE("GPL v2"); -- cgit v1.3.1